Here we follow the notation of Ref. [1]}, which is defined as
\(\langle  {\bf a}_2 , i , j \rangle  \equiv \det \begin{pmatrix}a_{2,0} & v_{i,0} & v_{j,0} \\a_{2,1} & v_{i,1} & v_{j,1} \\a_{2,2} & v_{i,2} & v_{j,2}\end{pmatrix} ,\) 
